Magnetic ground states in solids often arise as a result of a delicate balance between competing factors. One currently active area of research in magnetic materials involves compounds in which longrange magnetic ordering at low temperatures is frustrated by the geometry of the crystalline lattice, a situation known as geometrical magnetic frustration. The number of systems known to display the effects of such frustration is growing, but those that are sufficiently simple from theoretical, chemical, and physical perspectives to allow for detailed understanding remain very few. A search for model compounds in this family has led us to the double perovskites Ba 2LnSbO6 and Sr2LnSbO6 (Ln ؍ Dy, Ho, and Gd) reported here. Ba 2DySbO6, Ba2HoSbO6, Sr2DySbO6, and Sr2HoSbO6 are structurally characterized by powder neutron diffraction at ambient temperature. The trivalent lanthanides and pentavalent antimony are found to be fully ordered in the double-perovskite arrangement of alternating octahedra sharing corner oxygens. In such a structure, the lanthanide sublattice displays a classical fcc arrangement, an edge-shared network of tetrahedra known to result in geometric magnetic frustration. No magnetic ordering is observed in any of these compounds down to temperatures of 2 K, and in the case of the Dy-based compounds in particular, frustration of the magnetic ordering is clearly present. Lanthanide-based double perovskites are proposed to be excellent model systems for the detailed study of geometric magnetic frustration. D espite decades of intensive investigation of the properties of magnetic materials, relatively little is known about compounds for which the long-range magnetic ordering of strongly interacting spins at low temperatures is frustrated by their geometric arrangement in the crystal lattice. The geometries of such frustrating lattices typically are based on corner-sharing triangles. This geometry makes long-range spin ordering that strictly satisfies near-neighbor pairwise antiferromagnetic interactions impossible. The resulting compromises in the spin orientations at low temperatures result in the existence of many energetically equivalent magnetic ground states (see refs. 1-4 for a review of the field). The 2D Kagomé lattice (named after a form of Japanese basket weaving) of corner-shared triangles of magnetic ions and its 3D extension to yield a corner-shared arrangement of magnetic tetrahedra (shown in Fig. 1) are of greatest current interest. Good examples of 2D Kagomé lattice magnetic compounds are found among the Jarosites (5, 6). The frustrating properties of the corner-sharing tetrahedron lattice have been particularly well studied for the magnetic lanthanide pyrochlores. Phenomena such as the formation of ''spin ice'' in Ho 2 Ti 2 O 7 and Dy 2 Ti 2 O 7 (7-11), the magnetic analogy of the geometric frustration of the ordering of hydrogen in ice at low temperatures, and the complex applied field͞temperature magnetic-phase diagram in Gd 2 Ti 2 O 7 (12) are examples of the consequences of geometric...